Accelerating interval matrix multiplication by mixed precision arithmetic

DOI Web Site 被引用文献1件 参考文献7件 オープンアクセス
  • Ozaki Katsuhisa
    Department of Mathematical Sciences, Shibaura Institute of Technology JST, CREST
  • Ogita Takeshi
    Division of Mathematical Sciences, Tokyo Woman's Christian University JST, CREST
  • Bünger Florian
    Institute for Reliable Computing, Hamburg University of Technology
  • Oishi Shin'ichi
    Faculty of Science and Engineering, Waseda University JST, CREST

説明

This paper is concerned with real interval arithmetic. We focus on interval matrix multiplication. Well-known algorithms for this purpose require the evaluation of several point matrix products to compute one interval matrix product. In order to save computing time we propose a method that modifies such known algorithm by partially using low-precision floating-point arithmetic. The modified algorithms work without significant loss of tightness of the computed interval matrix product but are about 30% faster than their corresponding original versions. The negligible loss of accuracy is rigorously estimated.

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